orbital railgun

This is not quite true. Newtonian physics means that every time you fire a shot from said orbital railgun you end up accelerating the railgun in the opposite direction - this requires thrusters or some such system to perform stationkeeping. If you do this, then you have to expend twice as much energy per shot - one set to fire, and one to counteract the resultant thrust.

The major advantages of a lunar-situated railgun are (as I see them) the following:

You have lots of time to see an attack coming, and the distance is such that a directed-energy attack is highly unlikely due to the fact that the power of an electromagnetic beam at any distance d compared to its intensity at start is (I think, IIRC) 1/d^3. It'd be reaaalllly hard to damage anything on the lunar surface with a beam weapon from Earth, not even taking into account the problems of motion.

It's actually a lot easier to shoot at something in orbit (especially LEO) than at something on the moon. The calculations are simpler. It's a lot easier to track your target. There's only one orbital state to track, not two.

The max power of the orbital railgun will swiftly run up against size limitations. The lunar version wouldn't have these problems, and could use less efficent/more redundant components.

The lunar railgun needs to use less power to achieve the same impact velocity. Why? Because you're taking advantage of the gravity well! You only need to boost to lunar escape velocity to have gravity do a great deal of the work as your projectile 'rides' the gravity well towards earth, trading its potential for kinetic energy all the way. Think of it as dropping something from the height of the moon, with only the last little bit of flight troubled by atmospheric resistance.

Support of the railgun (people, materials, solar power) is easier with a gravitational field and solid surface to walk on. Also, your staff can burrow to protect themselves from counterattack! You could even put the whole apparatus under the regolith if you were willing to spend the resources!

Admittedly, there are disadvantages, as Azure Monk points out. The big problems are, in my opinion:

Aiming. Your aiming calculations suddenly get really complex. It's highly unlikely this is going to be an assassination weapon (although, to be fair, I was never thinking of it that way). It's much more like an atomic bombardment tool without requiring atomic weapons...and if you vary the payload size down far enough, you could do some fairly high-energy but limited-spread damage due to the energy being kinetic and not radiative (at least at impact).

Reaction time. Shots would probably require lots of precalculation and 'monitoring' as they travelled, and perhaps even a manveuring system to correct for gravitational flux and error.

Fixed launching direction, if the 'gun' is big enough. You'd have to 'aim' entirely with timing, orbital dynamics and perhaps projectile maneuvering.

Oh, and to address one final point: If the railgun was laid fairly flat along the moon's surface, the energy transfer would be to the moon's rotational, not orbital velocity. I seriously doubt this would be a problem given the magnitudes we're talking, but if it was, just build another facing the opposite direction and alternate shots.

I'd also think that while stealthing the orbital railgun is workable, there's one problem. It's gonna generate one enormously fscking huge electromagnetic pulse when it fires. That's how it works.

Finally, since I'm not trying to hit moving targets, but level large immobile ones like, say, Cleveland, I can use minimal energy and just let the gravity well do my work. Unless someone's figured out how to move Cleveland out of the way, I'm probably okay. I *am* more vulnerable to interception; however, if I am using a lower shot energy and moving slowly, I can minimize any course correction burn intensity as well as have a better shot at avoiding detection of the initial shot. For a highly dramatized example, see Robert A. Heinlein's The Moon is a Harsh Mistress.

Now, if you're trying to destroy smaller targets, you're in even better shape...a really dense, heat-resistant small projectile (like, say, a tungsten or depleted uranium or osmium rod) can be launched at pretty high speed (or from really far out, but the math and response time get freaky). The havoc wreaked on a modern tank by another tank comes from a small penetrator of several kilos mass hitting the tank at between 1,000 and 2,500 m/sec. If you made a projectile that had an osmium sheath with a softer material under an ablative or frangible endcap, it would balloon out on impact with a hard object (you could tune that) and transfer all of its energy quickly. Tank rounds have been designed to do that. These rounds have no trouble dealing with atmospheric friction at those speeds for a couple of miles of STP; although the duration would be longer from orbit down, I bet it wouldn't be a big issue. Heck, if pieces of Skylab can hit the ground, made mostly of aircraft aluminum...:-)

Kuraijo: Not quite right. Terminal velocity assumes that the object is being acted on by gravity and air resistance as it accelerates, causing it to reach a plateau. While this would be true, if the projectile is accelerated outside the atmosphere to a high enough velocity, there won't be nearly enough atmospheric travel for it to slow down to anywhere near terminal velocity.

It's basically a question of how much force your railgun uses to fire a round:

The force (f) expended per shot depends on the mass of a round (rM), and the speed at which the round is fired (s):

f = rM * s

The effectiveness (E) of your railgun is determined by the force (f) used per round, and the total mass of the gun (gM) and whatever it is mounted on, be it a satellite or the moon. In the case of a lunar railgun, a low E means that the moon's orbit changes fatally after relatively few shots. A low E for an orbital railgun means that you need to expend a great amount of force to correct for orbit:

E = gM / f

CASE A: If your railgun requires relatively puny force to fire a round, an orbital railgun can correct its orbit without expending a great deal of energy.

Therefor, your railgun needs to accelerate rounds to extreme speeds. The round needs to reach its destination very quickly -- a few seconds at most. This means that the s variable of your force equation is very high.

This is also a property destruction device. It needs to be able to destroy property. If it was just an assassination weapon, it could use miniscule rounds. At extreme velocities, these would be sufficient to rip through human flesh and kill the target.

Not so with buildings. Many of the space-age construction materials we use today would suffer little damage from tiny rounds, even at insane velocities. (To roughly understand this concept, buy a gun. Shoot yourself in the leg. Now shoot a brick wall. Observe differences in reaction, particularly bleeding. This is a bastardization of the railgun/property damage concept, but it serves to demonstrate.) By the time the railgun was operational, we'd doubtless see advances in railgun resistant building materials, as well.

The rounds, therefor, also need to be fairly large. This makes the rM variable of the force equation large, as well.

As you probably know, when you multiply two very large numbers, you get a really huge number. f is now a really huge number. As a result, the railgun's effectiveness is greatly reduced.

Yes, it does, but we're repeatedly (many things we want to kill) accelerating fairly heavy projectiles to extreme velocities. Not just "really fast" velocities, EXTREME velocities. Extreme is a concept difficult to illustrate, due to its general overuse. For our purposes, pretend that "extreme" is a term several thousand orders of magnitude more severe than you perceive it to be.... OK, got it? Yeah, THAT fast.

Would this be enough to significantly affect the moon's orbit? Maybe. Maybe not. I'm betting it would, but I haven't punched the actual numbers -- I'd need a railgun spec sheet to do that.

There are other reasons why an earth orbit is a better choice than a lunar installment:

Defense. A moon-based railgun can be seen with a telescope, and its location is extremely predictable. It would be much easier to launch an attack against a known area on the clearly visible moon (and if you miss, you have a good chance of hitting it with "splash" damage) than it would be to attack a satellite with an unpredictable orbit that could only be detected with advanced technological means.

Target Opportunity. An orbital railgun can shift its orbit to arrive at any location above the earth in relatively little time. A lunar railgun has no control over its area of fire.

Service and Resupply. Earth's orbit is a lot closer than the moon. An orbital railgun could also be outfitted with landing apparatus to return to earth when necessary.

Ok. So you have an extremely deadly, accurate railgun in orbit that is virtually immune to attack and can decimate any target, anywhere on earth, within a matter of hours. It is easy to resupply and maintain... but it's expending twice as much energy per shot as it actually takes to fire the round. "Please," I conveniently make you ask, "can't you tell me how to avoid this?"

Simple. Decrease the railgun's speed in orbit prior to firing. The earth's gravitational force will take affect, pulling the weapon in a frightening, horrible descent toward earth. When you fire the rail, the gun will be violently hurled away from the earth, back into orbit. (And even if something goes horribly wrong, your railgun's firing platform will land on and crush your target, incinerating it in a fiery crater of doom!) The gravitational pull might not negate the entire force of the shot, but it will negate a significant portion. Just make sure you have damn good heat shielding.

Shooting things down from LEO: While you have to calculate two orbits (you can do it right now, so it shouldn't be too tough with the computing power of tomorrow) to attack a lunar railgun, the travel time of your counter attack allows for course corrections or evasive maneuvers. The orbital railgun can employ stealth technologies to make it difficult to track, and alter its course to make it difficult to predict. A lunar railgun is immobile other than the predictable orbit of the moon (it doesn't even rotate relative to earth!), which makes it easy to track as long as your computer can handle orbital calculations. Stealth technology is useless for a lunar railgun.

A lunar railgun uses less power: The moon is 240,000 miles away. LEO is 200 miles high. To hit a target in the same amount of time after firing, you need to expend 1200 times more energy, although it is somewhat less because of gravity. If you expend the same amount of energy, even with gravity, your reaction time will become so severe that the weapon will become useless against any mobile target.

However, the greater time a lunar railgun has to react to an attack is certainly a valid point. While it would be much easier to initiate an attack against a lunar railgun, the railgun's defensive systems would probably have hours to identify, track, and neutralize the threat. An orbital railgun would have minutes, if that, and would probably have little ability to neutralize the threat, due to size limitations of the satellite. The defensive strength of an orbital railgun is the difficulty in detecting it, but if someone had tracking technology that eclipsed your stealth technology, you'd pretty much be in for it.

Basically, each railgun is more defendable against certain kinds of attacks. Any attack based on inferior tracking technology will be more effective against a lunar railgun, but most missile weaponry would be pitifully ineffectual against a burrowing lunar railgun. However, the moon could be nuked.

Also, while your railgun's construction and maintenance crew will have an easier time on the moon, you'll have an easier time resupplying the railgun if it is in LEO, and your resupply vehicles will be less vulnerable. Which railgun is better in this situation is also largely a matter of what technologies the opposition has.

Ok, one final response to The Custodian:

As far as stealth goes: Yes, firing the railgun will make you detectable, but only for a short time, after which you can quickly change course.

I fail to see, however, how a railgun could be used to attack Cleveland. You have a huge ammount of kenetic force in the shell, but it is a relativley small object. Even if you were firing rounds that were a foot in diameter, you'd still have problems doing much real damage to Cleveland. Either you're proposing to use frickin' huge rounds, or just fire a TON of them.

In my opinion, this negates the advantages of a railgun. The whole point is that you can fire extremley fast, small shells, basicaly allowing you to snipe any target on earth, from orbit. A single shot being capible of killing any human target, and a few shots able to rend sufficient structural damage to a building to make it collapse. If you're just bombarding an area, you'd be better off with conventional payloads (bombs), and conventional payload delivery methods (planes). A railgun, especialy a lunar railgun, has a relativley small and infrequent fire opportunity, which makes it a poor method of delivery for a bombardment-style attack, and, similarly, solid metal rounds are a poor payload for a bombardment.

The moon is 240, 000 miles away from Earth. Although gravity grows much weaker as distance increases, lets assume that the Earth's gravity does not, giving you constant acceleration of 32 ft/sec/sec until the projectile impacts Earth.

This clearly fails to solve either of the problems with a propelled weapon. Firstly, there are too many possible variables for any computer to accurately calculate what will happen over the course of two and a half hours. Even if your computer could, the weapon would be useless for target assassination, especially since this figure assumes that there is no friction between the atmosphere and the projectile, and that earth's gravity is constant, neither of which are true. Earth's gravity would be orders of magnitude weaker near the moon, but presumably you could partially compensate by introducing a high (although not extreme) initial velocity.

Secondly, At a rate of 53 miles per second, your projectile would also suffer serious heat problems.

Although your weapon would be functional, it would be useless in killing any mobile target. The only advantage it would hold over a classic, orbital railgun is that you would need to expend less energy per shot. However, the massive calculations required (the earth will rotate quite significantly in two and a half hours) might make the total expenditure of resources about equal.

I don't know about YOU guys, but whenever I shoot my rail gun from either the moon or an orbital satelite I have the problem of the round burning up and being greatly deflected by the atmosphere. It seems that objects traveling at extremevelocities cause a lot of friction with all the air that surrounds the Earth, which causes them to burn up. Even when they DO make it to Earth, they've been deflected by the atmosphere so much that I don't know WHERE they're gonna hit, but it certainly isn't ever the spot I aimed for. I've given up on the rail gun idea; after spending all the billions of dollars on getting it constructed and placed on the moon (and on an orbital satelite) it occurred to me that I don't actually have to PROPEL an object at high speed, since the earth's gravity will pull it down faster than is neccesary anyway. Now I'm directing all my energy into a computer that can calculate where an object with a degrading orbit will land, so I can drop things on people from the moon (or my satelite in orbit).

to kind of parallel that, think of humans and water. if you are in a 747 flying at 26,000 ft and head straight down into water, it feels like concrete. same thing with light speed and atmosphere (or anything else with mass). an aside to this is also what you see in frank herbert's dune with the shield suits the various atreides and harkonnen fighters wore. you could plung a knife slowly through the force field, but they were impervious to high speed projectiles like bullets.

now that i have that off my chest, i will get to the juicy bits. about the only feasible way to destroy a target from orbit is with a slow moving projectile of considerable mass. like an asteroid. or a house-sized cargo container like that used in The Moon is a Harsh Mistress (damn good book, that one...). without enough mass, a projectile will just go up in a puff of smoke; no matter how fast you shoot it.

UNLESS you had some super-dense material to throw through the atmosphere. like something out of a neutron star or a pulsar. then you could accelerate it to near light speed. only one other problem. trying to hurl that dense of material will destroy any kind of apparatus you use. square one.

another problem with the reverse-acceleration you have detailed above: what kind of a device will stand up to two opposing, simultaneous, high energy mass accelerations? not too many. maybe the moon. not something you don't build with a little bit of over-engineering though...

Just one point. Terminal velocity. the problem isn't so much the fact that it burns up in the atmosphere (I'm pretty comfortable with the idea of a falling cattle prod, actually), but the fact that this friction with the atmosphere will limit its maximum speed. No matter how much initial input you give it, much of this energy wil be lost to friction. The only reason you would want to make it come out of the barrel so fast is to ensure that it hits the target ASAP, and thus simplify your calculations and increase the reliability of your lead target indicator.

And one question: are you people considering a geostationary railgun or an orbital one? It's kinda tricky eitehr way because any changes in velocity would affect the rifle's angular velocity and orbital height. Remember that in orbit v2 = GM/r (simplified equation). Change v and lots of other stuff changes.

Personally I find the idea of a lunar railgun more feasible. Realistically speaking, it's mainly because I don't like the idea that tons of space junk is out there floating at the same orbital height as my gun. Response time is also a factor, of course. Though the large orbital height will complicate calculations, also remember that the large mass of the moon will help to counteract the recoil momentum of the projectile, thus giving it a higher initial velocity. That will help alot.